Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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*this is multiple choice question* Determine which is a non-exact differential equation! (the answer can be more than one)
![### Differential Equations
Below are several differential equations. These can be used as practice problems or examples for studying how to solve different forms of differential equations. Review each equation and analyze the structure to determine the appropriate method for solution.
1. **Equation 1:**
\[
2xy \, dx + (x^2 + 1) \, dy = 0
\]
2. **Equation 2:**
\[
(2xy^2 + 2xy \, e^{2x} + e^{2x} y) \, dx + (2x^2 y + x \, e^{2x}) \, dy = 0
\]
3. **Equation 3:**
\[
2xy \, dy + (3x + 2y^2) \, dx = 0
\]
4. **Equation 4:**
\[
(x^2 + xy) \, dx + (y^2 + \frac{1}{2} x^2) \, dy = 0
\]
5. **Equation 5:**
\[
x^3 y^3 \, dx + x(1 + y^2) \, dy = 0
\]
6. **Equation 6:**
\[
(6xy - y^3) \, dx + (4y + 3x^2 - 3xy^2) \, dy = 0
\]
7. **Equation 7:**
\[
(y/x + 6x) \, dx + (\ln x - 2) \, dy = 0
\]
### Instructions for Use
- **Identify the Form:** Determine the type of differential equation you are working with (e.g., exact, linear, separable).
- **Methods of Solution:** Apply the appropriate method for solving, such as integration, finding an integrating factor, or using substitution.
- **Verify Solutions:** Check your work and ensure that the solution satisfies the equation.
- **Explore Graphical Solutions:** Where possible, use graphing tools to visualize the solutions and understand their behavior.](https://content.bartleby.com/qna-images/question/dd8f2877-2578-48c0-ab77-5dda294aaf93/5c985c8e-9493-4ce2-ba39-aea23652e193/dmbcf1s_processed.jpeg)
Transcribed Image Text:### Differential Equations
Below are several differential equations. These can be used as practice problems or examples for studying how to solve different forms of differential equations. Review each equation and analyze the structure to determine the appropriate method for solution.
1. **Equation 1:**
\[
2xy \, dx + (x^2 + 1) \, dy = 0
\]
2. **Equation 2:**
\[
(2xy^2 + 2xy \, e^{2x} + e^{2x} y) \, dx + (2x^2 y + x \, e^{2x}) \, dy = 0
\]
3. **Equation 3:**
\[
2xy \, dy + (3x + 2y^2) \, dx = 0
\]
4. **Equation 4:**
\[
(x^2 + xy) \, dx + (y^2 + \frac{1}{2} x^2) \, dy = 0
\]
5. **Equation 5:**
\[
x^3 y^3 \, dx + x(1 + y^2) \, dy = 0
\]
6. **Equation 6:**
\[
(6xy - y^3) \, dx + (4y + 3x^2 - 3xy^2) \, dy = 0
\]
7. **Equation 7:**
\[
(y/x + 6x) \, dx + (\ln x - 2) \, dy = 0
\]
### Instructions for Use
- **Identify the Form:** Determine the type of differential equation you are working with (e.g., exact, linear, separable).
- **Methods of Solution:** Apply the appropriate method for solving, such as integration, finding an integrating factor, or using substitution.
- **Verify Solutions:** Check your work and ensure that the solution satisfies the equation.
- **Explore Graphical Solutions:** Where possible, use graphing tools to visualize the solutions and understand their behavior.
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